J. Phys. IV France
Volume 116, October 2004
Page(s) 89 - 132

J. Phys. IV France 116 (2004) 89-132

DOI: 10.1051/jp4:2004116004

Simple theoretical tools for low dimension Bose gases

Y. Castin

Laboratoire Kastler Brossel, ENS, 24 rue Lhomond, 75 231 Paris, France

We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures larger than the chemical potential. In a second part, using a lattice model for the quantum field, we explain how to carefully generalize the usual Bogoliubov approach to study a degenerate and weakly interacting Bose gas in 1D, 2D or 3D in the regime of weak density fluctuations. In the last part, using the mapping to an ideal Fermi gas in second quantized formalism, we calculate and discuss physically the density fluctuations and the coherence properties of a gas of impenetrable bosons in 1D.

© EDP Sciences 2004